Directed Graphs & Binary Relations

A = [ 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 1 0 ] Compute the reachability matrix R by using washall's algorithm and also by using the formula R = A V A(2) V... V A(n)

I have three I cannot get

I have done several examples but these I cannot get right, I am not sure where I have made the mistake and I am confusing myself. a. List all the binary relations on the set {0,1}. b. List the reflexive relations on the set {0,1}. c. List the symmetric relations on the set {0,1}.

Counting

a. An office manager has four employees and nine reports to be done. In how many ways can the reports be assigned to the employees so that each employee has at least one report to do. b. Find the number of ways to put eight different books in five boxes, if no box is allowed to be empty.

Percents

A. You take a job that pays $25,000 annually. (a) How much do you earn n years from now if you receive a three percent raise each year? (b) How much do you earn n years from now if you receive a five percent raise each year? (c) How much do you earn n years from now if each year you receive a raise of $1000 plus two percent of your previous year's salary.

Random

In the questions I have below it says a bowl has eight ping pong balls numbered 1,2,2,3,4,5,5,5. You pick a ball at random. a. Find p(the number on the ball drawn is ≥ 3). b. Find p(the number on the ball drawn is even).